\item \subquestionpoints{10} \textbf{Laplace source.}

For this sub-question, we assume sources are distributed according to a standard Laplace distribution, i.e $s_i \sim \mathcal{L}(0,1)$. The Laplace distribution $\mathcal{L}(0,1)$ has PDF $f_{\mathcal{L}}(s) = \frac{1}{2}\exp\left(-|s|  \right)$. With this assumption, derive the update rule for a single example in the form
    
    $$ W := W + \alpha \left(\ldots\right).$$
    
